English

On Some Solutions to Hofstadter's $V$-Recurrence

Dynamical Systems 2020-02-11 v1 Chaotic Dynamics

Abstract

In this study, we explore the properties of certain solutions of Hofstadter's famous VV-recurrence, defined by the nested recurrence relation V(n)=V(nV(n1))+V(nV(n4))V(n)=V(n-V(n-1))+V(n-V(n-4)). First, we discover the nature behind a finite chaotic meta-Fibonacci sequence in terms of mortality in the VV-recurrence. Then, we construct a new kind of quasi-periodic solution which suggests a connection with another Hofstadter-Huber recursion, H(n)=H(nH(n2))+H(nH(n3))H(n)= H(n-H(n-2)) + H(n-H(n-3)).

Cite

@article{arxiv.2002.03396,
  title  = {On Some Solutions to Hofstadter's $V$-Recurrence},
  author = {Altug Alkan and Nathan Fox and Orhan Ozgur Aybar and Zehra Akdeniz},
  journal= {arXiv preprint arXiv:2002.03396},
  year   = {2020}
}
R2 v1 2026-06-23T13:35:47.166Z